If a coffee shop is still open in your neighborhood, here's how to pick up a cup safely:

Opt for drive-thru over in-store ordering, if possible, to limit contact with other people.
Use hand sanitizer after exchanging money and your cup. Wash your hands when you get home.
If possible, pour the to-go coffee out of the takeout container and into a clean mug from your own kitchen. Try stashing a thermal mug like this Contigo Insulated Travel Mug ($11.99, target.com) in your cup holder, and remember to pour very carefully and only when you're in "park" to avoid hot coffee spills).